The price of bitcoin could reach up to $40,000 as it becomes more accepted and easier to trade, billionaire investor Marc Lasry told CNBC on Wednesday.

"As it gets more into the mainstream, and as more markets end up allowing it to trade where it's freely tradable, to me that's more of the bet," Lasry said in a "Squawk Box" interview, adding that he sees bitcoin investors making five to 10 times their money in three to five years.

Lasry's day job is running the distressed debt investment firm that he helped start, Avenue Capital Group, which has about $9.6 billion in assets under management. But he said his bitcoin investments were made with his personal money.

The cryptocurrency has struggled to regain its footing after nearing $20,000 at the end of last year. Bitcoin lost more than half its value in the first six months of this year, according to data from Coinbase. However, the price of bitcoin spiked Tuesday, with pundits saying the jump had more to do with technical levels than any other catalyst.

Lasry expects bitcoin will have the most benefit for investors out of all the cryptocurrencies, saying, "The reason why I like bitcoin is because it's the one everybody is going to come to."

In addition to running Avenue Capital as chairman and CEO, Lasry owns a stake in the NBA's Milwaukee Bucks. He spoke to "Squawk Box" from the eighth annual CNBC and Institutional Investor Delivering Alpha conference.